\xiti
\begin{enhancedline}
\begin{xiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}, column{1}={18em}, rows={rowsep=0.5em}}
        \xxt{$3\sqrt{8} + 2\sqrt{32} - \sqrt{50}$；} & \xxt{$9\sqrt{3} - 7\sqrt{12} + 5\sqrt{48}$；} \\
        \xxt{$6 - \sqrt{\dfrac{3}{2}} - \sqrt{\dfrac{2}{3}}$；} & \xxt{$2\sqrt{\dfrac{2}{3}} + \sqrt{\dfrac{1}{6}} - \dfrac{1}{5}\sqrt{54}$；} \\
        \xxt{$\sqrt{\dfrac{1}{5}} + 2\sqrt{20} - 4\sqrt{\dfrac{4}{5}} - \dfrac{1}{5}\sqrt{5}$；} & \xxt{$\sqrt{12} + 3\sqrt{1\dfrac{1}{3}} - \sqrt{5\dfrac{1}{3}} - \dfrac{2}{3}\sqrt{48}$；} \\
    \end{tblr}

    \begin{tblr}{columns={colsep=0pt}, column{1}={18em}, rows={rowsep=0.5em}}
        \xxt{$2a\sqrt{27a} + 6a\sqrt{\dfrac{3a}{4}}$；} & \xxt{$\dfrac{1}{a}\sqrt{x^3} - \sqrt{\dfrac{1}{x}}$；} \\
        \xxt{$2a\sqrt{3ab^2} - \dfrac{b}{6}\sqrt{27a^3} + 2ab\sqrt{\dfrac{3}{4}a}$；} & \xxt{$5\sqrt{x^3y} - 2y\sqrt{xy} - 6\sqrt{xy} + \sqrt{\dfrac{y}{x}} + \sqrt{\dfrac{x}{y}}$。}
    \end{tblr}
\end{xiaoxiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \xxt{$(\sqrt{18} - \sqrt{98}) + (2\sqrt{75} - \sqrt{27})$；}

    \xxt{$(\sqrt{45} + \sqrt{18}) - (\sqrt{8} - \sqrt{125})$；}

    \xxt{$\left(\sqrt{12} - \sqrt{\dfrac{1}{2}} - 2\sqrt{\dfrac{1}{3}}\right) - 2\left(\sqrt{\dfrac{1}{8}} - \sqrt{18}\right)$；}

    \xxt{$\left(5\sqrt{\dfrac{1}{5}} - \dfrac{1}{2}\sqrt{20}\right) + \left(\dfrac{5}{4}\sqrt{\dfrac{4}{5}} - \sqrt{45}\right)$；}

    \xxt{$7\sqrt{a} - \left(a\sqrt{\dfrac{1}{a}} - 4\sqrt{ab^2}\right)$；}

    \xxt{$\left(\dfrac{2}{3}x\sqrt{9x} + 6x\sqrt{\dfrac{y}{x}}\right) + \left(\sqrt{\dfrac{x}{y}} - x^2\sqrt{\dfrac{1}{x}}\right)$。}

\end{xiaoxiaotis}

\xiaoti{}%
\begin{xiaoxiaotis}%
    \xxt[\xxtsep]{当 $x = 7$ 时，求下列代数式的值：\\
        \hspace*{2em} $\sqrt{x + 5} + \sqrt{x - 4} - \sqrt{4x - 1}$；
    }

    \xxt{当 $x = 4$， $y = 16$ 时，求下列代数式的值：\\
        \hspace*{2em} $\sqrt{x^3 + x^2y + \dfrac{1}{4}xy^2} + \sqrt{\dfrac{1}{4}x^2y + xy^2 + y^3}$。
    }

\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep=0.5em}}
        \xxt{$\sqrt{15} \cdot \sqrt{1\dfrac{2}{3}}$；} & \xxt{$6\sqrt{1\dfrac{3}{5}} \cdot \left(-5\sqrt{2\dfrac{2}{5}}\right)$；} \\
        \xxt{$\dfrac{1}{3}\sqrt{12x} \cdot 2\sqrt{3x}$；} & \xxt{$10a^2\sqrt{ab} \cdot 5\sqrt{\dfrac{1}{a}}$；} \\
        \xxt{$\dfrac{1}{3}\sqrt{30} \cdot 40\sqrt{\dfrac{1}{2}} \cdot \dfrac{3}{2}\sqrt{2\dfrac{2}{3}}$；}
            & \xxt{$3\sqrt{\dfrac{a}{x}} \cdot \left(-2\sqrt{\dfrac{x}{a}}\right) \cdot \sqrt{\dfrac{b}{a}}$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep=0.5em}}
        \xxt{$(\sqrt{12} + 5\sqrt{8}) \cdot \sqrt{3}$；} & \xxt{$3\sqrt{2} \cdot \left(2\sqrt{12} - 4\sqrt{\dfrac{1}{8}} + 3\sqrt{48}\right)$；} \\
        \xxt{$\left(\sqrt{xy} - 2\sqrt{\dfrac{y}{x}} + \sqrt{\dfrac{x}{y}}\right) \cdot \sqrt{xy}$；} & \xxt{$(\sqrt{a^3b} + \sqrt{ab^3} - ab) \cdot \sqrt{ab}$；} \\
        \SetCell[c=2]{l}\xxt{$\dfrac{3}{4}\left(\dfrac{\sqrt{5}}{3} - 2\sqrt{3}\right) - \dfrac{\sqrt{3}}{2}(1 - 4\sqrt{3} + 3\sqrt{5})$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}, column{1}={18em}}
        \xxt{$(2\sqrt{3} - 2) (3\sqrt{6} + \sqrt{2})$；} & \xxt{$(\sqrt{27} + \sqrt{28}) (\sqrt{12} - \sqrt{63})$；} \\
        \xxt{$(2\sqrt{3} - 3\sqrt{2} + \sqrt{6}) (\sqrt{6} - 5\sqrt{3})$；} & \xxt{$(\sqrt{5} + \sqrt{3} + \sqrt{2}) (\sqrt{5} - 2\sqrt{3} + \sqrt{2})$；} \\
        \xxt{$(\sqrt{x} + \sqrt{3}) (2\sqrt{x} + 3\sqrt{2})$；} & \xxt{$(x + y + 2\sqrt{xy}) (\sqrt{x} - \sqrt{y})$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}}
        \xxt{$(5\sqrt{3} + 4\sqrt{2}) (5\sqrt{3} - 4\sqrt{2})$；} & \xxt{$(7\sqrt{5} + 6\sqrt{7}) (6\sqrt{7} - 7\sqrt{5})$；} \\
        \xxt{$(3\sqrt{2} + \sqrt{48}) (\sqrt{18} - 4\sqrt{3})$；} \\
        \SetCell[c=2]{l}\xxt{$\left(\dfrac{-b + \sqrt{b^2 - 4ac}}{2a}\right) \left(\dfrac{-b - \sqrt{b^2 - 4ac}}{2a}\right) \quad (b^2 - 4ac > 0)$；} \\
        \xxt{$(7\sqrt{3} + 2\sqrt{7})^2$；} & \xxt{$(4 - 5\sqrt{3})^2$；} \\
        \xxt{$\left(3\sqrt{a} + 2\sqrt{\dfrac{x}{a}}\right)^2$；} & \xxt{$\left(3\sqrt{1\dfrac{2}{3}} - \sqrt{1\dfrac{4}{5}}\right)^2$；} \\
        \xxt{$(\sqrt{2} + \sqrt{3} - \sqrt{6}) (\sqrt{2} - \sqrt{3} - \sqrt{6})$；} \\
        \SetCell[c=2]{l}\xxt{$(\sqrt{x + y} + \sqrt{x - y})^2 + (\sqrt{x + y} - \sqrt{x - y})^2 \quad (x > y)$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{把下列各式的分母有理化：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}, column{1,2}={12em}, rows={rowsep=0.5em}}
        \xxt{$\dfrac{3}{\sqrt{5}}$；} & \xxt{$\dfrac{\sqrt{2}}{3\sqrt{40}}$；} & \xxt{$\dfrac{7n}{3\sqrt{n}}$；} \\
        \xxt{$\dfrac{\sqrt{x - 1}}{\sqrt{x + 1}} \; (x > 1)$；} & \xxt{$\dfrac{1}{\sqrt{5} - 2}$；} & \xxt{$\dfrac{\sqrt{5}}{\sqrt{3} + \sqrt{2}}$；} \\
        \xxt{$\dfrac{\sqrt{3} + \sqrt{15}}{\sqrt{3} - \sqrt{15}}$；} & \xxt{$\dfrac{3\sqrt{5} - 2\sqrt{3}}{3\sqrt{5} + 2\sqrt{3}}$；} & \xxt{$\dfrac{2\sqrt{x + 2} + 3\sqrt{x - 2}}{\sqrt{x + 2} + \sqrt{x - 2}} \; (x > 2)$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep=0.5em}}
        \xxt{$\sqrt{\dfrac{1}{45}} \div \dfrac{3}{2}\sqrt{2\dfrac{2}{3}}$；} & \xxt{$\sqrt{20a} \div \dfrac{2}{3}\sqrt{b}$；} \\
        \xxt{$\sqrt{15} \cdot \sqrt{1\dfrac{2}{3}} \div \sqrt{24}$；} & \xxt{$\sqrt{\dfrac{a}{b}} \cdot \left(\sqrt{\dfrac{b}{a}} \div \sqrt{\dfrac{1}{b}}\right)$；} \\
        \xxt{$\left(\sqrt{48} + \dfrac{1}{2}\sqrt{1\dfrac{1}{2}}\right) \div \sqrt{27}$；} & \xxt{$\left(\dfrac{3}{4}\sqrt{7} - \sqrt{6}\right) \div \left(\sqrt{5} - \sqrt{3}\right)$；} \\
        \xxt{$(7\sqrt{2} + 2\sqrt{6}) \div (2\sqrt{6} - 7\sqrt{2})$；} & \xxt{$\sqrt{15} \div \left(\dfrac{1}{\sqrt{3}} + \dfrac{1}{\sqrt{2}}\right)$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{求下列各式的值（精确到 $0.01$）：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep=0.5em}}
        \xxt{$\dfrac{\sqrt{5} - 1}{\sqrt{2}}$；} & \xxt{$\dfrac{\sqrt{2}}{3 - \sqrt{3}}$；} \\
        \xxt{$\dfrac{3}{2\sqrt{2}} - \dfrac{2}{\sqrt{5} + 1}$；} & \xxt{$\dfrac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$；} \\
        \xxt{$\left(\dfrac{2}{x + 1}\right)^2$，其中 $x = \sqrt{3}$；} & \xxt{$\dfrac{a - 4b}{\sqrt{a} - 2\sqrt{b}}$，其中 $a = 6$，$b = 5$。}
    \end{tblr}
\end{xiaoxiaotis}


\xiaoti{}%
\begin{xiaoxiaotis}%
    \xxt[\xxtsep]{已知 $x = \dfrac{2}{\sqrt{3} - 1}$，求 $x^2 - x + 1$ 的值；}

    \xxt{已知 $x = 2 + \sqrt{3}$，求 $\dfrac{3x^2 - 2x + 5}{2x- 7}$ 的值。}

\end{xiaoxiaotis}


\xiaoti{化简：}
\begin{xiaoxiaotis}

    \xxt{$\dfrac{1}{\sqrt{3} + \sqrt{2}} + \dfrac{1}{\sqrt{2} + 1} - \dfrac{2}{\sqrt{3} + 1}$；}

    \xxt{$\dfrac{5}{4 - \sqrt{11}} + \dfrac{1}{3 + \sqrt{7}} - \dfrac{6}{\sqrt{7} - 2} - \dfrac{\sqrt{7} - 5}{2}$；}

    \xxt{$\dfrac{1}{y}\sqrt{x - y} + \dfrac{x}{\sqrt{x - y}} - \dfrac{1}{x - y}\sqrt{(x - y)^3} \; (x > y)$；}

    \xxt{$\dfrac{\sqrt{x + 1} - \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}} + \dfrac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}$。}

\end{xiaoxiaotis}

\end{xiaotis}
\end{enhancedline}
